Question:
The coordinates of the circumcentre of the triangle with vertices $(2, 3), (4, -1) $ and $ (4, 3) $ are
The coordinates of the circumcentre of the triangle with vertices $(2, 3), (4, -1) $ and $ (4, 3) $ are
Updated On: May 12, 2024
- (2, 3)
- (1, 3)
- (3, 1)
- (3, 2)
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The Correct Option is C
Solution and Explanation
Coordinates of A, B, Care (2, 3) (4, -1), (4, 3). respectively.
Slope $m_1$ of BC is $ \frac{3 -(-1)}{4-4} =\infty$
Slope $m_2$ of AC is $ \frac{3 -3}{4-2} = 0$
$ \therefore \:\:\:\Delta ABC $ is right angled at C (4, 3)
$ \therefore$ Circumcentre of $\Delta ABC$ is the mid-point of the hypotenuse AB which is
$ \left( \frac{4 + 2}{2} , \frac{3 -1}{2} \right)$ i.e.., $(3,1) $
Slope $m_1$ of BC is $ \frac{3 -(-1)}{4-4} =\infty$
Slope $m_2$ of AC is $ \frac{3 -3}{4-2} = 0$
$ \therefore \:\:\:\Delta ABC $ is right angled at C (4, 3)
$ \therefore$ Circumcentre of $\Delta ABC$ is the mid-point of the hypotenuse AB which is
$ \left( \frac{4 + 2}{2} , \frac{3 -1}{2} \right)$ i.e.., $(3,1) $
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